Kelly formula
Kelly % = (b × p - q) ÷ b
Strategy Tools
LiveKelly Criterion Calculator | Full & Half Kelly Stakes | XYES
Use this free Kelly Criterion calculator to size full Kelly, half Kelly or quarter Kelly stakes from bankroll, odds and estimated win probability.
Full / Half / Quarter KellyBankroll percentageFree · no signup
Quick answer
What does this Kelly calculator actually tell you?
- Kelly is a stake-sizing model, not a prediction model.
- It uses odds, estimated win probability and bankroll to estimate how much to stake.
- Positive EV should be checked first; Kelly only sizes the stake after the price looks worth betting.
- Many bettors use half Kelly or quarter Kelly because probability estimates are rarely perfect.
Kelly criterion calculator
Enter bankroll, odds and your estimated win probability
Start with the full Kelly number, then scale it down with half Kelly or quarter Kelly when the edge is thin or your estimate is uncertain.
Start here
The Kelly Criterion estimates how much of your bankroll to stake
Kelly starts with one practical question: if your probability estimate is right, how much is too much to risk? It is not a prediction model. It is a staking model that helps you avoid overbetting weak edges and underbetting stronger ones.
See the three checks
- 1Check whether your win probability is above the break-even probability implied by the odds.
- 2Calculate the full Kelly stake as a percentage of bankroll.
- 3Use half Kelly or quarter Kelly to reduce drawdowns and make the staking plan easier to follow.
- 1Check whether your win probability is above the break-even probability implied by the odds.
- 2Calculate the full Kelly stake as a percentage of bankroll.
- 3Use half Kelly or quarter Kelly to reduce drawdowns and make the staking plan easier to follow.
Common scenarios
Start with an example, then replace it with your own bankroll and line.
Apply
Apply：$10,000 bankroll · 2.10 odds · 52% win probability · Half Kelly
Odds format
Kelly fraction
Conservative stake · Selected Kelly 4.18%
Recommended stake $418
How to use it
How to calculate full, half and quarter Kelly stake size
Enter bankroll, decimal, fractional or American odds and your estimated win probability, choose full Kelly, half Kelly or quarter Kelly, then review stake size and risk status.
- 1
Enter bankroll
- 2
Enter odds and win probability
- 3
Choose Kelly fraction
- 4
Review stake and risk
Formula and example
How does the Kelly Criterion formula calculate stake size?
Kelly converts the price and your probability estimate into a bankroll percentage. The better the edge, the larger the theoretical stake; if there is no edge, the answer is no bet.
Net odds
b = decimal odds - 1
Win / lose probability
p = estimated win probability, q = 1 - p
Quick example: $10,000 · 2.10 · 52% · Half Kelly
- At decimal odds 2.10, b = 1.10.
- Estimated win probability is 52%, so losing probability is 48%.
- Full Kelly = (1.10 × 52% - 48%) ÷ 1.10 = 8.36%.
- Half Kelly = 4.18%, so a $10,000 bankroll gives a stake of about $418.
Choose the fraction
Full Kelly vs half Kelly vs quarter Kelly
Full Kelly is the theoretical answer. In real betting, many players use a smaller fraction because estimates are rarely perfect and drawdowns are easier to handle at lower stakes.
Full Kelly
Highest varianceBest reserved for very strong probability estimates and a bankroll that can handle sharp swings.
Fastest theoretical growth, but the rough patches can feel brutal.
Half Kelly
Medium varianceA common default for positive-EV fixed-odds betting when you want room for estimate error.
Cuts the full Kelly stake in half while keeping the bet tied to the edge.
Quarter Kelly
Lower varianceThin edges, volatile markets or players who want a cautious starting point.
Slower growth, but easier to follow over a long sample.
Custom fraction
Depends on settingsPlayers with their own bankroll rules or staking limits.
Consider starting between 25% and 50% Kelly instead of jumping to full Kelly.
Three staking checks
After calculating Kelly, check these three points
Negative Kelly means skip
If your win probability is below the break-even line, Kelly returns zero or negative stake size. Do not force the bet.
Full Kelly is volatile
Full Kelly is theoretically aggressive. Half Kelly or quarter Kelly is usually easier to tolerate over losing streaks.
Probability error is the main risk
Kelly is sensitive to win probability. If your estimate is uncertain, reduce the fraction or skip the bet.
Strategy context
How are Kelly Criterion and expected value connected?
Expected value answers whether the price is worth betting. Kelly answers how much of bankroll to stake if you decide to bet. Positive EV is a long-term estimate; it does not mean full Kelly is automatically appropriate.
Positive EV but thin margin
If full Kelly is only 1% or 2%, the edge is thin and a small probability mistake can erase the value.
Half Kelly for smoother bankroll swings
Half Kelly sacrifices some theoretical growth in exchange for lower drawdown and a more practical staking plan.
Negative Kelly is not a reason to stake more
A negative result means the odds do not compensate for the risk under your estimate. Wait for a better price or improve the estimate.
FAQ
Kelly Criterion calculator questions
Answers about Kelly formula, full Kelly, half Kelly, negative Kelly, positive EV staking and probability-estimation risk.
What is the Kelly Criterion?
The Kelly Criterion is a bankroll-management formula that uses odds and estimated win probability to calculate what percentage of bankroll to stake. It is a bet-sizing model, not a way to predict the next result.
How do you calculate Kelly bet size?
The common formula is Kelly % = (b × p - q) ÷ b. b is decimal odds minus 1, p is estimated win probability and q is losing probability. Multiply the result by bankroll to get full Kelly stake size.
Is half Kelly better than full Kelly?
Half Kelly is often more practical than full Kelly because it lowers drawdowns and leaves more room for imperfect probability estimates. Full Kelly has higher theoretical growth, but the bankroll swings are much harder to tolerate.
When should I use quarter Kelly?
Quarter Kelly is useful when the edge is thin, the market is volatile or your probability estimate is only rough. It grows more slowly than half Kelly, but it is easier to stick with over a long sample.
Why does Kelly say no bet?
Kelly says no bet when your estimated win probability is below the break-even probability implied by the odds. Under that assumption, the price does not pay enough for the risk.
Does positive EV mean I should use full Kelly?
No. Positive EV only means the bet has positive theoretical value under your assumptions. If the estimate is uncertain or variance is high, half Kelly, quarter Kelly or no bet may be more appropriate.
Can Kelly Criterion be used for sports betting?
Yes, but only if you have a reliable win-probability estimate. In sports betting, the hard part is usually estimating probability better than the market, not applying the formula.
Can Kelly Criterion be used for casino games?
It can be used as a mathematical example, but most casino games have a built-in house edge and are not positive EV. Without a real edge, Kelly will usually recommend no bet.
How is Kelly different from expected value?
Expected value checks whether the price is worth betting. Kelly uses the same odds and probability assumptions to estimate how much of bankroll to stake if you decide to bet.
What happens if my win probability estimate is wrong?
Kelly is very sensitive to probability estimates. Overestimating win probability can produce an oversized stake, so many players use half Kelly or quarter Kelly to reduce that risk.
What bankroll should I use for Kelly staking?
Use the bankroll reserved for this betting strategy, not your full personal balance. Mixing everyday funds, long-term savings or unrelated betting pools into the bankroll will make the Kelly stake too large.
Does Kelly work with American odds?
Yes. Convert American odds to decimal odds first, then apply the same Kelly formula. This calculator supports American odds input directly, alongside decimal and fractional odds.
Why do many bettors use fractional Kelly?
Many bettors use fractional Kelly because the full Kelly number assumes your probability estimate is accurate. Half Kelly or quarter Kelly reduces drawdowns when the estimate is rough, the market moves or variance is high.
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